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Merge remote-tracking branch 'origin/main' into mpz_realloc

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xiaoh105
2025-06-21 22:08:51 +08:00
parent f8af2cf004 77e1460ebc
commit 1e627cdb84
8 changed files with 1470 additions and 18 deletions
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projects/lib/gmp_goal.v
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@ -15,11 +15,11 @@ Local Open Scope Z_scope.
Local Open Scope sets.
Local Open Scope string.
Local Open Scope list.
Require Import Coq.ZArith.ZArith.
Local Open Scope Z_scope.
Import naive_C_Rules.
Local Open Scope sac.
Definition Zmax := Z.max.
(*----- Function gmp_abs -----*)
Definition gmp_abs_safety_wit_1 :=
@ -61,7 +61,7 @@ forall (b_pre: Z) (a_pre: Z) ,
[| (a_pre <= b_pre) |]
&& emp
|--
[| (b_pre = (Zmax (a_pre) (b_pre))) |]
[| (b_pre = (Z.max (a_pre) (b_pre))) |]
&& emp
.
@ -70,7 +70,7 @@ forall (b_pre: Z) (a_pre: Z) ,
[| (a_pre > b_pre) |]
&& emp
|--
[| (a_pre = (Zmax (a_pre) (b_pre))) |]
[| (a_pre = (Z.max (a_pre) (b_pre))) |]
&& emp
.
@ -1753,6 +1753,904 @@ forall (xp_pre: Z) (val: Z) (cap: Z) (n: Z) ,
** (store_undef_uint_array_rec xp_pre n cap )
.
(*----- Function mpn_add_1 -----*)
Definition mpn_add_1_safety_wit_1 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) ,
[| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& ((( &( "i" ) )) # Int |->_)
** (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** ((( &( "b" ) )) # UInt |-> b_pre)
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
** (store_uint_array rp_pre cap2 l2 )
|--
[| (0 <= INT_MAX) |]
&& [| ((INT_MIN) <= 0) |]
.
Definition mpn_add_1_safety_wit_2 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
[| (l'' = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32))) ((app (l') ((cons (a) (nil)))))) )
** ((( &( "i" ) )) # Int |-> i)
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** ((( &( "b" ) )) # UInt |-> 0)
** (store_uint_array ap_pre n_pre l_2 )
** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
|--
[| ((i + 1 ) <= INT_MAX) |]
&& [| ((INT_MIN) <= (i + 1 )) |]
.
Definition mpn_add_1_safety_wit_3 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
[| (l'' = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32))) ((app (l') ((cons (a) (nil)))))) )
** ((( &( "i" ) )) # Int |-> i)
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** ((( &( "b" ) )) # UInt |-> 1)
** (store_uint_array ap_pre n_pre l_2 )
** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
|--
[| ((i + 1 ) <= INT_MAX) |]
&& [| ((INT_MIN) <= (i + 1 )) |]
.
Definition mpn_add_1_entail_wit_1 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) ,
[| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l_2)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array_rec rp_pre 0 cap2 l2 )
** (store_uint_array rp_pre 0 nil )
** (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|--
EX (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l: (@list Z)) ,
[| (0 <= 0) |]
&& [| (0 <= n_pre) |]
&& [| (list_store_Z_compact l val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (0) (l)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b_pre * (Z.pow (UINT_MOD) (0)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = 0) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l_2)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre 0 l' )
** (store_uint_array_rec rp_pre 0 cap2 l'' )
.
Definition mpn_add_1_entail_wit_2 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
[| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l_2 )
** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
** ((( &( "i" ) )) # Int |-> i)
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
** ((( &( "b" ) )) # UInt |-> b)
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
|--
[| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& ((( &( "b" ) )) # UInt |-> b)
** (store_uint_array ap_pre n_pre l_2 )
** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
** ((( &( "i" ) )) # Int |-> i)
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
.
Definition mpn_add_1_entail_wit_3_1 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (b: Z) (l''_2: (@list Z)) (l'_2: (@list Z)) (val2_2: Z) (val1_2: Z) (l_3: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
[| (l''_2 = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32)) < b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_3 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_3)) val1_2 ) |]
&& [| (list_store_Z l'_2 val2_2 ) |]
&& [| ((val2_2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1_2 + b_pre )) |]
&& [| ((Zlength (l'_2)) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l_2)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32))) ((app (l'_2) ((cons (a) (nil)))))) )
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** (store_uint_array ap_pre n_pre l_3 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|--
EX (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l: (@list Z)) ,
[| (0 <= (i + 1 )) |]
&& [| ((i + 1 ) <= n_pre) |]
&& [| (list_store_Z_compact l val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) ((i + 1 )) (l)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (1 * (Z.pow (UINT_MOD) ((i + 1 ))) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = (i + 1 )) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l_2)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre (i + 1 ) l' )
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l'' )
.
Definition mpn_add_1_entail_wit_3_2 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (b: Z) (l''_2: (@list Z)) (l'_2: (@list Z)) (val2_2: Z) (val1_2: Z) (l_3: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
[| (l''_2 = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32)) >= b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_3 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_3)) val1_2 ) |]
&& [| (list_store_Z l'_2 val2_2 ) |]
&& [| ((val2_2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1_2 + b_pre )) |]
&& [| ((Zlength (l'_2)) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l_2)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array rp_pre (i + 1 ) (replace_Znth (i) ((unsigned_last_nbits (((Znth i l_3 0) + b )) (32))) ((app (l'_2) ((cons (a) (nil)))))) )
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** (store_uint_array ap_pre n_pre l_3 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|--
EX (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l: (@list Z)) ,
[| (0 <= (i + 1 )) |]
&& [| ((i + 1 ) <= n_pre) |]
&& [| (list_store_Z_compact l val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) ((i + 1 )) (l)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (0 * (Z.pow (UINT_MOD) ((i + 1 ))) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = (i + 1 )) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l_2)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre (i + 1 ) l' )
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l'' )
.
Definition mpn_add_1_return_wit_1 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l_2: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l: (@list Z)) (i: Z) ,
[| (i >= n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l_2)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
|--
EX (val': Z) ,
[| ((val' + (b * (Z.pow (UINT_MOD) (n_pre)) ) ) = (val + b_pre )) |]
&& (mpd_store_Z_compact ap_pre val n_pre cap1 )
** (mpd_store_Z rp_pre val' n_pre cap2 )
.
Definition mpn_add_1_partial_solve_wit_1 :=
forall (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) ,
[| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (mpd_store_Z_compact ap_pre val n_pre cap1 )
** (store_uint_array rp_pre cap2 l2 )
|--
[| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (mpd_store_Z_compact ap_pre val n_pre cap1 )
** (store_uint_array rp_pre cap2 l2 )
.
Definition mpn_add_1_partial_solve_wit_2_pure :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) ,
[| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& ((( &( "i" ) )) # Int |-> 0)
** (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** ((( &( "b" ) )) # UInt |-> b_pre)
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
** (store_uint_array rp_pre cap2 l2 )
|--
[| ((Zlength (l2)) = cap2) |]
.
Definition mpn_add_1_partial_solve_wit_2_aux :=
forall (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) ,
[| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre cap2 l2 )
|--
[| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array rp_pre cap2 l2 )
** (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
.
Definition mpn_add_1_partial_solve_wit_2 := mpn_add_1_partial_solve_wit_2_pure -> mpn_add_1_partial_solve_wit_2_aux.
Definition mpn_add_1_partial_solve_wit_3 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
[| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
|--
[| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (((ap_pre + (i * sizeof(UINT) ) )) # UInt |-> (Znth i l_2 0))
** (store_uint_array_missing_i_rec ap_pre i 0 n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
.
Definition mpn_add_1_partial_solve_wit_4_pure :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& ((( &( "b" ) )) # UInt |-> 0)
** (store_uint_array ap_pre n_pre l_2 )
** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
** ((( &( "i" ) )) # Int |-> i)
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
|--
[| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
.
Definition mpn_add_1_partial_solve_wit_4_aux :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
|--
[| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
** (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
.
Definition mpn_add_1_partial_solve_wit_4 := mpn_add_1_partial_solve_wit_4_pure -> mpn_add_1_partial_solve_wit_4_aux.
Definition mpn_add_1_partial_solve_wit_5_pure :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& ((( &( "b" ) )) # UInt |-> 1)
** (store_uint_array ap_pre n_pre l_2 )
** ((( &( "r" ) )) # UInt |-> (unsigned_last_nbits (((Znth i l_2 0) + b )) (32)))
** ((( &( "i" ) )) # Int |-> i)
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
** ((( &( "n" ) )) # Int |-> n_pre)
** ((( &( "ap" ) )) # Ptr |-> ap_pre)
** ((( &( "rp" ) )) # Ptr |-> rp_pre)
|--
[| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
.
Definition mpn_add_1_partial_solve_wit_5_aux :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) ,
[| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
** (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
|--
[| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
** (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
.
Definition mpn_add_1_partial_solve_wit_5 := mpn_add_1_partial_solve_wit_5_pure -> mpn_add_1_partial_solve_wit_5_aux.
Definition mpn_add_1_partial_solve_wit_6 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
[| (l'' = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** (store_uint_array rp_pre (i + 1 ) (app (l') ((cons (a) (nil)))) )
** (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|--
[| (l'' = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) < b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (((rp_pre + (i * sizeof(UINT) ) )) # UInt |->_)
** (store_uint_array_missing_i_rec rp_pre i 0 (i + 1 ) (app (l') ((cons (a) (nil)))) )
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
.
Definition mpn_add_1_partial_solve_wit_7 :=
forall (b_pre: Z) (n_pre: Z) (ap_pre: Z) (rp_pre: Z) (cap2: Z) (cap1: Z) (l2: (@list Z)) (val: Z) (l: (@list Z)) (b: Z) (l'': (@list Z)) (l': (@list Z)) (val2: Z) (val1: Z) (l_2: (@list Z)) (i: Z) (a: Z) (l''': (@list Z)) ,
[| (l'' = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** (store_uint_array rp_pre (i + 1 ) (app (l') ((cons (a) (nil)))) )
** (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
|--
[| (l'' = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& [| ((unsigned_last_nbits (((Znth i l_2 0) + b )) (32)) >= b) |]
&& [| (0 <= b) |]
&& [| (b <= UINT_MAX) |]
&& [| (i < n_pre) |]
&& [| (0 <= i) |]
&& [| (i <= n_pre) |]
&& [| (list_store_Z_compact l_2 val ) |]
&& [| (n_pre <= cap1) |]
&& [| (list_store_Z (sublist (0) (i) (l_2)) val1 ) |]
&& [| (list_store_Z l' val2 ) |]
&& [| ((val2 + (b * (Z.pow (UINT_MOD) (i)) ) ) = (val1 + b_pre )) |]
&& [| ((Zlength (l')) = i) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& [| ((Zlength (l2)) = cap2) |]
&& [| (cap2 >= n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (cap2 <= 100000000) |]
&& [| (n_pre > 0) |]
&& [| (n_pre <= cap1) |]
&& (((rp_pre + (i * sizeof(UINT) ) )) # UInt |->_)
** (store_uint_array_missing_i_rec rp_pre i 0 (i + 1 ) (app (l') ((cons (a) (nil)))) )
** (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** (store_uint_array ap_pre n_pre l_2 )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
.
Definition mpn_add_1_which_implies_wit_1 :=
forall (n_pre: Z) (ap_pre: Z) (cap1: Z) (val: Z) ,
(mpd_store_Z_compact ap_pre val n_pre cap1 )
|--
EX (l: (@list Z)) ,
[| (n_pre <= cap1) |]
&& [| ((Zlength (l)) = n_pre) |]
&& [| (cap1 <= 100000000) |]
&& [| (list_store_Z_compact l val ) |]
&& (store_uint_array ap_pre n_pre l )
** (store_undef_uint_array_rec ap_pre n_pre cap1 )
.
Definition mpn_add_1_which_implies_wit_2 :=
forall (rp_pre: Z) (cap2: Z) (l2: (@list Z)) ,
[| ((Zlength (l2)) = cap2) |]
&& (store_uint_array rp_pre cap2 l2 )
|--
[| ((Zlength (l2)) = cap2) |]
&& (store_uint_array_rec rp_pre 0 cap2 l2 )
** (store_uint_array rp_pre 0 nil )
.
Definition mpn_add_1_which_implies_wit_3 :=
forall (n_pre: Z) (rp_pre: Z) (cap2: Z) (l'': (@list Z)) (l': (@list Z)) (i: Z) ,
[| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& (store_uint_array rp_pre i l' )
** (store_uint_array_rec rp_pre i cap2 l'' )
|--
EX (a: Z) (l''': (@list Z)) ,
[| (l'' = (cons (a) (l'''))) |]
&& [| (0 <= i) |]
&& [| (i < n_pre) |]
&& [| (n_pre <= cap2) |]
&& (store_uint_array_rec rp_pre (i + 1 ) cap2 l''' )
** (store_uint_array rp_pre (i + 1 ) (app (l') ((cons (a) (nil)))) )
.
(*----- Function mpz_clear -----*)
Definition mpz_clear_return_wit_1_1 :=
@ -2851,6 +3749,27 @@ Axiom proof_of_mpn_normalized_size_return_wit_1_2 : mpn_normalized_size_return_w
Axiom proof_of_mpn_normalized_size_partial_solve_wit_1 : mpn_normalized_size_partial_solve_wit_1.
Axiom proof_of_mpn_normalized_size_partial_solve_wit_2 : mpn_normalized_size_partial_solve_wit_2.
Axiom proof_of_mpn_normalized_size_which_implies_wit_1 : mpn_normalized_size_which_implies_wit_1.
Axiom proof_of_mpn_add_1_safety_wit_1 : mpn_add_1_safety_wit_1.
Axiom proof_of_mpn_add_1_safety_wit_2 : mpn_add_1_safety_wit_2.
Axiom proof_of_mpn_add_1_safety_wit_3 : mpn_add_1_safety_wit_3.
Axiom proof_of_mpn_add_1_entail_wit_1 : mpn_add_1_entail_wit_1.
Axiom proof_of_mpn_add_1_entail_wit_2 : mpn_add_1_entail_wit_2.
Axiom proof_of_mpn_add_1_entail_wit_3_1 : mpn_add_1_entail_wit_3_1.
Axiom proof_of_mpn_add_1_entail_wit_3_2 : mpn_add_1_entail_wit_3_2.
Axiom proof_of_mpn_add_1_return_wit_1 : mpn_add_1_return_wit_1.
Axiom proof_of_mpn_add_1_partial_solve_wit_1 : mpn_add_1_partial_solve_wit_1.
Axiom proof_of_mpn_add_1_partial_solve_wit_2_pure : mpn_add_1_partial_solve_wit_2_pure.
Axiom proof_of_mpn_add_1_partial_solve_wit_2 : mpn_add_1_partial_solve_wit_2.
Axiom proof_of_mpn_add_1_partial_solve_wit_3 : mpn_add_1_partial_solve_wit_3.
Axiom proof_of_mpn_add_1_partial_solve_wit_4_pure : mpn_add_1_partial_solve_wit_4_pure.
Axiom proof_of_mpn_add_1_partial_solve_wit_4 : mpn_add_1_partial_solve_wit_4.
Axiom proof_of_mpn_add_1_partial_solve_wit_5_pure : mpn_add_1_partial_solve_wit_5_pure.
Axiom proof_of_mpn_add_1_partial_solve_wit_5 : mpn_add_1_partial_solve_wit_5.
Axiom proof_of_mpn_add_1_partial_solve_wit_6 : mpn_add_1_partial_solve_wit_6.
Axiom proof_of_mpn_add_1_partial_solve_wit_7 : mpn_add_1_partial_solve_wit_7.
Axiom proof_of_mpn_add_1_which_implies_wit_1 : mpn_add_1_which_implies_wit_1.
Axiom proof_of_mpn_add_1_which_implies_wit_2 : mpn_add_1_which_implies_wit_2.
Axiom proof_of_mpn_add_1_which_implies_wit_3 : mpn_add_1_which_implies_wit_3.
Axiom proof_of_mpz_clear_return_wit_1_1 : mpz_clear_return_wit_1_1.
Axiom proof_of_mpz_clear_return_wit_1_2 : mpz_clear_return_wit_1_2.
Axiom proof_of_mpz_clear_return_wit_1_3 : mpz_clear_return_wit_1_3.